Celestial Phenomena : Moon analemma

[Calculus]

You all know and saw pictures of a sun analemma, but have you heard of the moon analemma ?
To my knowledge, no actual picture has ever been taken of this phenomenon.
They are different from lunar month to lunar month (due to the very complex motion of the moon). And yes, they repeat every lunar month. In my gallery, you can see 2 examples of such a lunar analemma.
To get these images, the difficulty was to calculate the duration of the mean lunar day: 24h 50min 28.3272s. I let you come up with the reasoning (not that difficult).

More to come...